Decidability of Scott's Model as an Ordered $\mathbb{Q}$-Vectorspace

Journal of Symbolic Logic 62 (3):917-924 (1997)
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Abstract

Let $L = \langle, +, h_q, 1\rangle_{q \in \mathbb{Q}}$ where $\mathbb{Q}$ is the set of rational numbers and $h_q$ is a one-place function symbol corresponding to multiplication by $q$. Then the $L$-theory of Scott's model for intuitionistic analysis is decidable.

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A new model for intuitionistic analysis.Philip Scowcroft - 1990 - Annals of Pure and Applied Logic 47 (2):145-165.
More on real algebra in scott's model.Philip Scowcroft - 1986 - Annals of Pure and Applied Logic 30 (3):277-291.
A transfer theorem in constructive real algebra.Philip Scowcroft - 1988 - Annals of Pure and Applied Logic 40 (1):29-87.

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